When the tungsten filament in a 75 W, 120 V light bulb reaches 2040° C, 75 W of
ID: 1682913 • Letter: W
Question
When the tungsten filament in a 75 W, 120 V light bulb reaches 2040° C, 75 W of electric power is used to produce light and heat.Find the current through the filament under these conditions, which are established very shortly after the light is turned on.
Find the filament current when the light is first turned on, assuming an initial filament temperature of 20° C.
Find the power used when the light is first turned on, assuming an initial filament temperature of 20° C.
Estimate the time needed to heat the filament to 2040° C. The filament has a mass of 0.043 g and a specific heat of 0.032 cal/g-C°.
Explanation / Answer
voltage V = 120 V t1 = 20° C t2 = 2040° C t2 - t1 = 2020° C when the filament at 2040° C : ------------------------------------- power used p = 75 W current through the filament i = p/V = 75/120 = 0.625 A resistance R = V/i = 120/0.625 = 192 O --------------------------------------------------------------------------------- temperature coefficient a for tungsten at 20° C = 0.0046 ° C-1 R2 = R1[1 + a(t2-t1)] 192 = R1[1 + (0.0046*2020)] 192 = R1*10.292 R1 = 18.65 O current i = V/R1 = 120/18.65 = 6.434 A ------------------------------------------------------------------------------- power p = V*i = 120*6.434 = 772.08 W ------------------------------------------------------------------------------- now we have to calculate time t: Given that m = 0.043 g = 0.000043 Kg specific heat of tungsten s = 0.032 cal/g-C° = 0.032*4.186*1000 j/Kg-°C = 133.952 j/Kg-°C we know that p = (m*s*?t)/t so time t = (m*s*?t)/p = (0.000043*133.952*2020)/772.08 = 0.015 sRelated Questions
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